1. Suppose (27.625 base 10) is represented using a 16-bit Floating Point Format where 1 bit is for the sign bit, 5 bits is for exponent and 10 bits is for mantissa. What is the exponent? Do not involve a space character when you type your answer
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1. Suppose (27.625 base 10) is represented using a 16-bit Floating Point Format where 1 bit is for the sign bit, 5 bits is for exponent and 10 bits is for mantissa. What is the exponent? Do not involve a space character when you type your answer.
2. Suppose (-27.625 base 10) is represented using a 16-bit Floating Point Format where 1 bit is for the sign bit, 5 bits is for exponent and 10 bits is for mantissa. What is the the result? Do not involve a space character when you type your answer.
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- Consider an 8-bit floating point format. In this representation 4 bits are reserved for the mantissa and 3 bits are reserved for the exponent and 1 bit is reserved for the sign of the number. The exponent of the number is stored with a bias = 3. Express the decimal number 4.75 in this 8 bit floating point format. Write down the next bigger representable number in decimal base. B If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.75 Express the decimal number 4.75 in this 8 bit floating point format. [10] b) Write down the next bigger representable number in decimal base. [7.5] c) If you would be conducting the following operation using this 8 bit floating point format what would the result of the following calculation be ? 4.75 + 0.05 - 4.756. Assume we are using a simple model for floating-point representation similar to the one used in Chapter 2 of the textbook which has a 14-bit format, 5 bits for the exponent with a bias of 15 (not 16 as in the textbook), a normalized mantissa of 8 bits, and a single sign bit. Show how the computer would represent the numbers 12.125 using this representation.Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14- bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number): Convert 22.375 to the floating-point binary representation. Your Answer:
- Question 4: Floating Point Below is a simplified 8 bit floating point format, with 1 bit for sign, 4 bits for the fraction, and 3 bits for the exponent. (Format: Sffffeee = (-1)$x0.ffffx2(eee-4)) For each example, write the decimal equivalent. %3D 1. 1 0101 110 Decimal: 2. 0 1111 111 Decimal: 3. 0 0001 000 Decimal:Consider the half-precision floating-point format, which has five bits for the exponent and ten bits for the significand. Find the decimal (i.e., base 10) number represented by the following bits in the half-precision floating- point format: (a) 0100110001110000. (b) 1000001111 1111. (c) 0111110000000000.Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating- point numbers in part a by changing one of the numbers so they are both expressed using the same power of 2. c) Show how the computer would represent the sum in part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.
- We are using the simple model for floating point representation which is a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit. Show step by step how the computer would represent the following numbers using this floating- point format | a. -6.47510 i. Convert it into a binary number ii. Normalize this binary number iii. Fill up the fieldsAssume we have a byte system for the fixed number representation (the whole number is presented with 8-bits (one byte) and the fractional part is presented with 2-bits), find the 2's complement of 0110 0010.01 The answer should be formatted as a fractional 2's complement binary number representation with the exact format of the answer that is required of this particular calculation. I've gotten an answer of 1001 1110.00 but it says its wrong please help1. In a binary coded decimal (BCD) system, 4 bits are used to represent a decimal digit from 0 to 9. For example, 3710 is written as 00110111BCD. (a) Write 28910 in BCD (b) Convert 100101010001BCD to decimal (c) Convert 01101001BCD to binary (d) Explain why BCD might be a useful way to represent numbers
- Number representation and overflow] Consider the following 8 bit binary number numbers below: A = 11010111 B = 10011101 a. What is the value of A in decimal if we interpreted A as an unsigned number? b. What is the value of B in decimal if we interpreted B as a two's complement number? c. In two's complement representations for both A and B: i. What is the value of (A + B)? Indicate if there is an overflow? ii. What is the value of (B - A)? Indicate if there is an overflow?Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number): Convert -43.0735 to the floating-point binary representation. (Remember we learned "implied one" format in the lecture)4. A computer stores real numbers in floating point format in 8-bit words. The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next two bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa. What is the base-10 number (10100111)2 given 8-bit format?